List of top Quantitative Aptitude Questions on Divisibility and Factors asked in CAT

The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is

The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is

Let \(n\) be the least positive integer such that \(168\) is a factor of \(1134^n\) . If \(m\) is the least positive integer such that \(1134^n\) is a factor of \(168^m\) , then \(m+ n \) equals

(1134)ⁿ is divisible by 168. (168)^m is divisible by (1134)ⁿ. Find the minimum value of n + m

For some natural number n,assume that \((15,000)!\) is divisible by \((n!)!\) The largest possible value of n is

How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?